A bag contains 4 red marbles, 1 green one, 1 lavender one, 3 yellows, and 2 orange marbles. HINT [See Example 7.] How many sets of five marbles include at most one of the yellow ones?

266

Step-by-step explanation:

Red marbles = 4

Green marbles = 1

Lavender marbles = 1

Yellow marbles = 3

Orange marbles = 2

To pick 5 marbles with at most 1 yellow, we can pick 5 non-yellow marbles or (4 non-yellow marble and 1 yellow marble).

Picking 5 non-yellow marbles

There are 4 + 1 + 1 + 2 = 8 non-yellow marbles.

The number of ways of picking any 5 is

Picking 4 non-yellow marble and 1 yellow marble

The number of ways of picking any 4 non-yellow marbles is

The number of ways of picking any 1 yellow marble from 3 is

Number of ways for both =

Total number of picking 5 marbles with at most 1 yellow

Therefore, total number of ways = 56 + 210 = 266

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3